The IR/UV Connection in the Non-Commutative Gauge Theories

TL;DR

This paper investigates the unusual infrared behavior in non-commutative gauge theories, revealing that anomalies depend on supersymmetry and are absent in certain highly supersymmetric models, challenging conventional renormalization assumptions.

Contribution

It provides a detailed analysis of IR/UV mixing effects at one loop in non-commutative gauge theories, highlighting the role of supersymmetry in mitigating anomalies.

Findings

Poles in the non-commutativity parameter Theta cause IR discrepancies.

Supersymmetric theories lack these poles, reducing anomalies.

Non-commutative super Yang Mills with 16 supercharges shows no anomalies.

Abstract

Quantum field theory on non-commutative spaces does not enjoy the usual ultraviolet-infrared decoupling that forms the basis for conventional renormalization. The high momentum contributions to loop integrations can lead to unfamiliar long distance behavior which can potentially undermine naive expectations for the IR behavior of the theory. These "anomalies" involve non-analytic behavior in the noncommutativity parameter Theta making the limit Theta goes to zero singular. In this paper we will analyze such effects in the one loop approximation to gauge theories on non-commutative space. We will see that contrary to expectations poles in Theta do occur and lead to large discrepancies between the expected and actual infrared behavior. We find that poles in Theta are absent in supersymmetric theories. The "anomalies" are generally still present, but only at the logarithmic level. A notable exception is non-commutative super Yang Mills theory with 16 real supercharges in which anomalous effects seem to be absent altogether.